Method of determining the electrical properties of the earth by processing electromagnetic signals propagated through the earth from a capacitor

Abstract

A method of processing electromagnetic signals which are injected into the earth from a capacitor and subsequently detected after reflection from subsurface layers, in order to determine the physical and electrical properties of those layers. The method is based on an iterative process which models the earth as a series of vertically stacked horizontal layers, each characterized by its physical properties of depth beneath the surface and thickness, and its electrical properties of resistivity (or conductivity) and relative dielectric constant. An initial propagation model which specifies the electrical properties of a particular layer or set of layers is constructed and applied to a model input pulse to produce a predicted return pulse which results from the reflection and/or transmission of the input pulse at the boundaries of the layer(s). The predicted return pulse is then compared to actual return pulse data which is selected so as to roughly correspond to a return pulse produced at the location of the modeled layer(s). The result of the comparison forms the basis for adaptively varying the parameters of the propagation model in a manner which is intended to increase the correlation between the predicted return pulse and the actual data. Repetition of the method for different layers or additional locations permits the electrical characteristics of the earth beneath a specified region to be determined. Knowledge of these characteristics can be used to infer the type of geologic formation responsible for transforming the input pulse into the received pulse.

I claim: 
     
       1. A method for processing a return electromagnetic pulse that has propagated through a subterranean formation from a capacitor, including the steps of: (a) selecting an initial geoelectric column model which determines a set of filter coefficients indicative of one or more electromagnetic properties of a set of vertically stacked horizontal layers of the subterranean formation;   (b) generating a simulated return pulse by applying the filter coefficients to a model input electromagnetic pulse, where the simulated return pulse represents response of the formation to application of the model input electromagnetic pulse; and   (c) generating a modified geoelectric column model which results in increased correlation between the return electromagnetic pulse and a simulated return pulse predicted by the modified geoelectric column model, relative to correlation between the return electromagnetic pulse and a simulated return pulse predicted by the initial geoelectric column model.   
     
     
       2. A method for processing a return electromagnetic pulse that has propagated through a subterranean formation from a capacitor, including the steps of: (a) selecting a geoelectric column model, said model determining a set of filter coefficients indicative of properties of vertically stacked horizontal layers of the subterranean formation;   (b) generating a simulated return pulse by applying the filter coefficients to a model input electromagnetic pulse, where the simulated return pulse represents a response of the formation, measured at a first location of the formation during a first time window after application of the model input electromagnetic pulse to the first location;   (c) correlating a detected portion of the return electromagnetic pulse with the simulated return pulse, wherein said detected portion of the return electromagnetic pulse is detected during the first time window after application of an input electromagnetic pulse to the formation;   (d) generating a modified geoelectric column model defined by modified filter coefficients selected for increasing correlation during a subsequent repetition of step (c); and   (e) repeating steps (b) through (d) using the modified filter coefficients in place of the filter coefficients, until a desired degree of correlation is achieved in the final repetition of step (c).   
     
     
       3. The method of claim 2, also including the step of: (f) applying the input electromagnetic pulse to the subterranean formation from a capacitor at said first location.   
     
     
       4. The method of claim 3, wherein step (f) includes the steps of: disposing capacitor plates having a largest dimension L in direct contact with the formation at said first location, to form an earth capacitor comprising the plates and a region of the formation near the plates; and   applying a short voltage pulse across the capacitor plates to transmit the input electromagnetic pulse into the formation, wherein for each frequency component of the input electromagnetic pulse, the largest dimension L satisfies the relation Re[kL]<1, where k is the wavenumber in the formation of said frequency component, and further, wherein the short voltage pulse has frequency components in a broad band extending from below 1 MHz to above 100 MHz.   
     
     
       5. The method of claim 4, also including the steps of: detecting a return portion of the input electromagnetic pulse after said input electromagnetic pulse has propagated through the formation in response to application of the short voltage pulse, and wherein said portion of the return electromagnetic pulse processed in step (c) includes only frequency components of the detected return portion in a frequency window having an upper frequency less than 25 MHz.   
     
     
       6. The method of claim 2, also including the steps of: (g) after step (e), selecting an expanded geoelectric column model comprising an expanded set of filter coefficients, said expanded set including the modified filter coefficients generated during the final repetition of step (d), and additional filter coefficients indicative of an additional layer of the subterranean formation;   (h) after step (g) repeating steps (b) through (e) using the expanded set of filter coefficients to generate a modified, expanded geoelectric column model.   
     
     
       7. The method of claim 2, also including the steps of: (g) after step (e), repeating steps (b) through (e), with the simulated return pulse representing a response of the formation measured at the first location during a second time window after application of the model input electromagnetic pulse to the first location, and with the detected portion of the return electromagnetic pulse detected during the second time window after application of the input electromagnetic pulse to the formation.   
     
     
       8. The method of claim 2, wherein step (d) includes the step of applying a spectrum normalizing filter to the modified filter coefficients, and wherein step (c) includes the step of applying a spectrum normalizing filter to the detected portion of the return electromagnetic pulse before correlating said detected portion of the return electromagnetic pulse with the simulated return pulse. 
     
     
       9. The method of claim 2, also including the step of: determining a resistivity model from the modified geoelectric column model determined during the final repetition of step (d), said resistivity model determining a resistivity of each of the vertically stacked horizontal layers.   
     
     
       10. The method of claim 2, also including the step of: determining a dielectric coefficient model from the modified geoelectric column model determined during the final repetition of step (d), said dielectric coefficient model determining a dielectric coefficient of each of the vertically stacked horizontal layers.   
     
     
       11. The method of claim 2, also including the step of: determining an electrical property of each of said vertically stacked horizontal layers as a function of frequency, from the modified geoelectric column model determined during the final repetition of step (d).   
     
     
       12. A method for determining electromagnetic properties of a subterranean formation, including the steps of: (a) transmitting an electromagnetic pulse into the formation by disposing capacitor plates having a largest dimension L, in direct contact with the earth formation to form an earth capacitor comprising the plates and a region of the earth formation near the plates, and applying a short voltage pulse across the capacitor plates to transmit electromagnetic radiation into the earth formation, wherein for each frequency component of the electromagnetic radiation, the largest dimension L satisfies the relation Re[kL]<1, where k is the wavenumber in the earth formation of said frequency component, and further, wherein the short voltage pulse has frequency components in a broad band extending from below 1 MHz to above 100 MHz;   (b) detecting a return electromagnetic pulse that has propagated through the earth formation in response to application of the short voltage pulse; and   (c) processing only frequency components of the return electromagnetic pulse, in a frequency window having an upper frequency less than 25 MHz, which have propagated into the earth formation to a penetration depth much greater than on the order of several hundred feet, to determine a geoelectric column model which determines one or more electromagnetic properties of a set of vertical layers of the formation.   
     
     
       13. The method of claim 12, wherein step (c) includes the steps of: selecting an initial geoelectric column model which determines a set of filter coefficients indicative of one or more electromagnetic properties of a set of vertically stacked horizontal layers of the formation;   generating a simulated return pulse by applying the filter coefficients to a model input electromagnetic pulse, where the simulated return pulse represents response of the formation to application of the model input electromagnetic pulse; and   generating a modified geoelectric column model which results in increased correlation between said frequency components of the return electromagnetic pulse and a simulated return pulse predicted by the modified geoelectric column model, relative to correlation between said frequency components of the return electromagnetic pulse and a simulated return pulse predicted by the initial geoelectric column model, and identifying said modified geoelectric column model as said geoelectric column model.